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2800 x 2800 chessboard

Source: China Girls Math Olympiad 2008, Problem 7

August 26, 2008
combinatorics

Problem Statement

On a given 2008×2008 2008 \times 2008 chessboard, each unit square is colored in a different color. Every unit square is filled with one of the letters C, G, M, O. The resulting board is called harmonic if every 2×2 2 \times 2 subsquare contains all four different letters. How many harmonic boards are there?
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